Kelvin-Helmholtz instability in non-Newtonian complex plasma

In dusty plasma, viscosity plays a vital role on the dynamics of dust flow. For Newtonian regime, shear flow takes parabolic form. Strong velocity shear exists in the boundary layer and viscosity for its diffusive nature drives this shear energy to midstream flow to launch the instability. Dusty plasma shows non-Newtonian behaviour where viscosity ($\eta$) depends on velocity shear rate ($\gamma$). Different values of $\epsilon$ (ratio of equilibrium plasma temperature and melting temperature) generate different types of velocity profile and corresponding viscosity profile with shear rate. With numerical eigenvalue analysis, it is shown that shear thinning property enhances the Kelvin-Helmholtz instability but shear thickening property stabilizes it [D. Banerjee et. al., Phys. Plasmas {\bf {20}}, 073702 (2013)]. The maximum growth rate is observed for incompressible limit and the effect of compressibility is found to decrease the growth rate. The dispersion effect of Poisson's equation is also reported.